论文标题
一类计数时间序列模型，将复合泊松inar和Ingarch模型团结起来
A class of count time series models uniting compound Poisson INAR and INGARCH models
论文作者
论文摘要
INAR（整数值自回归）和Ingarch（Ingger值GARCH）模型是计数时间序列建模的最常用方法之一，但已在很大程度上不同的文献中进行了研究。在本文中，引入了新的一类广义整数值ARMA（Ginarma）模型，该模型统一了大量的复合泊松和Ingarch流程。研究了它的随机特性，包括平稳性和几何牙齿性。特别注意Inar（$ p $）模型的概括，该模型与Innarch（P）扩展到Ingarch（P，Q）模型的扩展相同。对于推断，我们考虑基于力矩的估计和受正算法启发的最大可能性推理方案。拟议类的模型具有自然的解释为随机流行过程，在整个文章中，该过程用于说明我们的论点。在一个案例研究中，该类别的不同实例（包括已建立的模型和新引入的模型）都应用于德国巴伐利亚州的每周麻疹和腮腺炎案例。
INAR (integer-valued autoregressive) and INGARCH (integer-valued GARCH) models are among the most commonly employed approaches for count time series modelling, but have been studied in largely distinct strands of literature. In this paper, a new class of generalized integer-valued ARMA (GINARMA) models is introduced which unifies a large number of compound Poisson INAR and INGARCH processes. Its stochastic properties, including stationarity and geometric ergodicity, are studied. Particular attention is given to a generalization of the INAR($p$) model which parallels the extension of the INARCH(p) to the INGARCH(p, q) model. For inference, we consider moment-based estimation and a maximum likelihood inference scheme inspired by the forward algorithm. Models from the proposed class have a natural interpretation as stochastic epidemic processes, which throughout the article is used to illustrate our arguments. In a case study, different instances of the class, including both established and newly introduced models, are applied to weekly case numbers of measles and mumps in Bavaria, Germany.
